Lecture on SUSY Gauge Theories and Integrable Systems

1997 ◽  
Vol 11 (26n27) ◽  
pp. 3093-3124
Author(s):  
A. Marshakov
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Integrable Systems ◽  
Gauge Theories ◽  
Toda Chain ◽  
Quantum Field ◽  
Standard Quantum ◽  
Integrable Equations ◽  
Complex Curves ◽  
Periodic Toda Chain

I consider main features of the formulation of the finite-gap solutions to integrable equations in terms of complex curves and generating 1-differential. The example of periodic Toda chain solutions is considered in detail. Recently found exact nonperturbative solutions to [Formula: see text] SUSY gauge theories are formulated using the methods of the theory of integrable systems and where possible the parallels between standard quantum field theory results and solutions to the integrable systems are discussed.

scholarly journals AN ALGORITHMIC APPROACH TO QUANTUM FIELD THEORY

2006 ◽  
Vol 21 (03) ◽  
pp. 405-447 ◽  
Author(s):  
MASSIMO DI PIERRO
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Path Integral ◽  
Gauge Theories ◽  
Quantum Field ◽  
Algorithmic Approach ◽  
Main Emphasis ◽  
Lattice Computation ◽  
Theoretical Foundations ◽  
Minimal Residual

The lattice formulation provides a way to regularize, define and compute the Path Integral in a Quantum Field Theory. In this paper, we review the theoretical foundations and the most basic algorithms required to implement a typical lattice computation, including the Metropolis, the Gibbs sampling, the Minimal Residual, and the Stabilized Biconjugate inverters. The main emphasis is on gauge theories with fermions such as QCD. We also provide examples of typical results from lattice QCD computations for quantities of phenomenological interest.

Field Theory in Particle Physics, Volume 1 and Quantum Field Theory and Gauge Theories of Strong and Electroweak Interactions

Physics Today ◽  
1987 ◽  
Vol 40 (12) ◽  
pp. 86-88
Author(s):  
B. de Wit ◽  
J. Smith ◽  
Lewis H. Ryder ◽  
Peter Becher ◽  
Manfred Böhm ◽  
...  
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Particle Physics ◽  
Gauge Theories ◽  
Quantum Field ◽  
Electroweak Interactions

scholarly journals The principle of stationary variance in quantum field theory

2014 ◽  
Vol 29 (05) ◽  
pp. 1450026 ◽  
Author(s):  
Fabio Siringo
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Quantum Mechanics ◽  
Quantum System ◽  
Quantum Electrodynamics ◽  
Best Approximation ◽  
Variational Approach ◽  
Heisenberg Model ◽  
Gauge Theories ◽  
Quantum Field

The principle of stationary variance is advocated as a viable variational approach to quantum field theory (QFT). The method is based on the principle that the variance of energy should be at its minimum when the state of a quantum system reaches its best approximation for an eigenstate. While not too much popular in quantum mechanics (QM), the method is shown to be valuable in QFT and three special examples are given in very different areas ranging from Heisenberg model of antiferromagnetism (AF) to quantum electrodynamics (QED) and gauge theories.

scholarly journals Gauge Theories and the Standard Model

2020 ◽  
pp. 7-33
Author(s):  
Guido Altarelli ◽  
Stefano Forte
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Standard Model ◽  
Gauge Theories ◽  
Quantum Field ◽  
Link Type ◽  
The Standard Model ◽  
Strong Sector ◽  
Introductory Textbooks ◽  
Symmetry Structure

AbstractThis chapter, Chaps. 10.1007/978-3-030-38207-0_3 and 10.1007/978-3-030-38207-0_4 present a self-contained introduction to the Standard Model of fundamental interactions, which describes in the unified framework of gauge quantum field theories all of the fundamental forces of nature but gravity: the strong, weak, and electromagnetic interactions. This set of chapters thus provides both an introduction to the Standard Model, and to quantum field theory at an intermediate level. The union of the three chapters can be taken as a masters’ level course reference, and it requires as a prerequisite an elementary knowledge of quantum field theory, at the level of many introductory textbooks, such as Vol. 1 of Aitchison-Hey, or, at a somewhat more advanced level, Maggiore. The treatment is subdivided into three parts, each corresponding to an individual chapter, with more advanced field theory topics introduced along the way as needed. Specifically, this chapter presents the general structure of the Standard Model, its field content, and symmetry structure. This involves an introduction to non-abelian gauge theories both at the classical and quantum level. Also, it involves a discussion of spontaneous symmetry breaking and the Higgs mechanism, that play a crucial role in the architecture of the Standard Model, and their interplay with the quantization of gauge theories. Chapter 10.1007/978-3-030-38207-0_3 then presents the electroweak sector of the Standard Model. This requires introducing the concepts of CP violation and mixing, and of radiative corrections. Finally, Chap. 10.1007/978-3-030-38207-0_4 presents the strong sector of the theory, which requires a more detailed treatment of renormalization and the renormalization group.

scholarly journals Emerging Quantum Fields Embedded in the Emergence of Spacetime

2018 ◽  
Author(s):  
Hans Diel
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Causal Model ◽  
Space Time ◽  
Quantum Field ◽  
Quantum Fields ◽  
Standard Quantum ◽  
Discrete Spacetime ◽  
Feynman Rules ◽  
Space Point

Based on a local causal model of the dynamics of curved discrete spacetime, a causal model of quantum field theory in curved discrete spacetime is described. At the elementary level, space(-time) is assumed to consists of interconnected space points. Each space point is connected to a small discrete set of neighbor space points. Density distribution of the space points and the lengths of the space point connections depend on the distance from the gravitational sources. This leads to curved spacetime in accordance with general relativity. Dynamics of spacetime (i.e., the emergence of space and the propagation of space changes) dynamically assigns "in-connections" and "out-connections" to the affected space points.  Emergence and propagation of quantum fields (including particles) are mapped to the emergence and propagation of space changes by utilizing identical paths of in/out-connections. Compatibility with standard quantum field theory (QFT) requests the adjustment of the QFT techniques  (e.g., Feynman diagrams, Feynman rules, creation/annihilation operators), which typically apply to three in/out connections, to  n > 3  in/out connections. In addition, QFT computation in position space has to be adapted to a curved discrete space-time.

scholarly journals Emerging Quantum Fields Embedded in the Emergence of Spacetime

2018 ◽  
Author(s):  
Hans Diel
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Causal Model ◽  
Space Time ◽  
Quantum Field ◽  
Quantum Fields ◽  
Standard Quantum ◽  
Discrete Spacetime ◽  
Feynman Rules ◽  
Space Point

Based on a local causal model of the dynamics of curved discrete spacetime, a causal model of quantum field theory in curved discrete spacetime is described. On the elementary level, space(-time) is assumed to consists of interconnected space points. Each space point is connected to a small discrete set of neighboring space points. Density distribution of the space points and the lengths of the space point connections depend on the distance from the gravitational sources. This leads to curved spacetime in accordance with general relativity. Dynamics of spacetime (i.e., the emergence of space and the propagation of space changes) dynamically assigns "in-connections" and "out-connections" to the affected space points. Emergence and propagation of quantum fields (including particles) are mapped to the emergence and propagation of space changes by utilizing identical paths of in/out-connections. Compatibility with standard quantum field theory (QFT) requests the adjustment of the QFT techniques (e.g., Feynman diagrams, Feynman rules, creation/annihilation operators), which typically apply to three in/out connections, to n > 3 in/out connections. In addition, QFT computation in position space has to be adapted to a curved discrete space-time.

scholarly journals Emerging Quantum Fields Embedded in the Emergence of Spacetime

2018 ◽  
Author(s):  
Hans Diel
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Causal Model ◽  
Space Time ◽  
Quantum Field ◽  
Quantum Fields ◽  
Standard Quantum ◽  
Discrete Spacetime ◽  
Feynman Rules ◽  
Space Point

Based on a local causal model of the dynamics of curved discrete spacetime, a causal model of quantum field theory in curved discrete spacetime is described. At the elementary level, space(-time) is assumed to consists of interconnected space points. Each space point is connected to a small discrete set of neighbor space points. Density distribution of the space points and the lengths of the space point connections depend on the distance from the gravitational sources. This leads to curved spacetime in accordance with general relativity. Dynamics of spacetime (i.e., the emergence of space and the propagation of space changes) dynamically assigns "in-connections" and "out-connections" to the affected space points. Emergence and propagation of quantum fields (including particles) are mapped to the emergence and propagation of space changes by utilizing identical paths of in/out-connections. Compatibility with standard quantum field theory (QFT) requests the adjustment of the QFT techniques (e.g., Feynman diagrams, Feynman rules, creation/annihilation operators), which typically apply to three in/out connections, to n > 3 in/out connections. In addition, QFT computation in position space has to be adapted to a curved discrete space-time.

scholarly journals CONSTRUCTION OF A NON-STANDARD QUANTUM FIELD THEORY USING GENERALIZED HEISENBERG ALGEBRA

2002 ◽  
Vol 17 (05) ◽  
pp. 661-673 ◽  
Author(s):  
M. A. REGO-MONTEIRO ◽  
E. M. F. CURADO
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Heisenberg Algebra ◽  
Quantum Field ◽  
Ladder Operators ◽  
Standard Quantum ◽  
Heisenberg Type ◽  
Klein Gordon ◽  
Square Well ◽  
The One

We herein construct a Heisenberg-like algebra for the one-dimensional quantum free Klein–Gordon equation defined on the interval of the real line of length L. Using the realization of the ladder operators of this Heisenberg-type algebra in terms of physical operators we build a (3+1)-dimensional free quantum field theory based on this algebra. We introduce fields written in terms of the ladder operators of this Heisenberg-type algebra and a free quantum Hamiltonian in terms of these fields. The mass spectrum of the physical excitations of this quantum field theory is given by [Formula: see text], where n=1,2,… and mq is the mass of a particle in a relativistic infinite square-well potential of width L.

scholarly journals THE FULLING–DAVIES–UNRUH EFFECT IS MANDATORY: THE PROTON'S TESTIMONY

2002 ◽  
Vol 11 (10) ◽  
pp. 1573-1577 ◽  
Author(s):  
GEORGE E. A. MATSAS ◽  
DANIEL A. T. VANZELLA
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Confidence Level ◽  
Unruh Effect ◽  
Quantum Field ◽  
Standard Quantum ◽  
Accelerated Protons

We discuss the decay of accelerated protons and illustrate how the Fulling–Davies–Unruh effect is indeed mandatory to maintain the consistency of standard Quantum Field Theory. The confidence level of the Fulling–Davies–Unruh effect must be the same as that of Quantum Field Theory itself.

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